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General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Théories de la structure électronique, des transitions électroniques et de la liaison chimique, Theory of electronic structure, electronic transitions, and chemical binding, Atome, Atoms, Condition aux limites, Boundary conditions, Définition, Definition, Definición, Equation Lagrange, Lagrange equations, Espace temps, Space-time, Etude théorique, Theoretical study, Fonction onde, Wave functions, Méthode variationnelle Schwinger, Schwinger variational method, Structure électronique, and Electronic structure

The physics of a system is determined by a variation of the action integral, i.e., by a variation of the space-time volume integral of the Lagrange function. If one demands that the properties of an atom in a molecule be derived from physics, the atom must generate its own space-time volume, requiring that its boundaries be defined in real space. The variations in the action are related to the actions of generators of infinitesimal unitary transformations. In the general case, the action integral is altered by generators acting in both the spacelike and timelike surface bounding the space-time volume, whereas for a total isolated system, the physics is totally determined by their action in just the spacelike surfaces at the two time endpoints.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Etat condense: structure electronique, proprietes electriques, magnetiques et optiques, Condensed matter: electronic structure, electrical, magnetic, and optical properties, Etats électroniques, Electron states, Phénomènes collectifs, Collective effects, Echange, corrélation, réponses diélectrique et magnétique, plasmons, Exchange, correlation, dielectric and magnetic functions, plasmons, Supraconductivité, Superconductivity, Théories et modèles, Theory and models of superconducting state, Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.), Etude théorique, Theoretical study, Gaz électron, Electron gas, Interaction appariement, Pairing interactions, Paire Cooper, Cooper pairs, Phénomène collectif, Collective process, Fenómeno colectivo, Plasmon, Plasmons, Supraconductivité, and Superconductivity

It is demonstrated that in the plasma state of the homogeneous electron gas the time-reversal electron pair is stabilized. This nature survives even in the inhomogeneous electron gas, where the Bragg reflection at the lance points is not necessarily a stumbling block for electron pairing. Indeed, a critical radius rc exists around the lattice point, outside of which the time-reversal scattering state of the electron pair is guaranteed. The critical radius rc has an intrinsic importance as a measure of the coherence length ξ of the Cooper pair that exhibits the time-reversal symmetry.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Atome, Atoms, Energie totale, Total energy, Energía total, Etat fondamental, Ground states, Etude théorique, Theoretical study, Fonction corrélation, Correlation functions, Fonction onde, Wave functions, Méthode variationnelle, Variational methods, Numéro atomique, Atomic number, Optimisation, Optimization, Système 2 électrons, Two electron system, and Sistema 2 electrones

It is advocated to carry out an optimization procedure, which is based upon the variational method, in such a way that the optimum values of the variational parameters are expressed as functions of physical constants, such as the atomic number, Z. The three stages involved in this treatment are illustrated by the optimization of nine correlated wave functions, which describe the ground states of atomic two-electron systems. An analysis of the Z-expansions of the total energies associated with these functions leads to the concept of a class of variational functions.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Calculs de corrélation électronique pour les atomes et les molécules, Electron correlation calculations for atoms and molecules, Corrélation électronique, Electron correlation, Dimension base, Basis set size, Dimensión base, Energie, Energy, Etude théorique, Theoretical study, Fonction onde, Wave functions, Matrice densité, Density matrix, Ordre 2, Second order, Orden 2, Partition Moller Plesset, Moller Plesset partition, Partición Moller Plesset, Structure électronique, Electronic structure, Théorie perturbation, and Perturbation theory

The evaluation of second derivatives of the electronic energy for nonvariational wave functions using an energy functional is discussed. It is shown that, in certain cases, the formation of the first-order relaxed density matrix leads to an efficient algorithm for the calculation of second-order response properties. Detailed formulas are given for second-order MØller-Plesset perturbation theory.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Propriétés moléculaires et interactions avec les photons, Molecular properties and interactions with photons, Résonance et relaxation nucléaires, Nuclear resonance and relaxation, Calcul ab initio, Ab initio calculations, Composé organique, Organic compounds, Déplacement chimique, Chemical shift, Effet substituant, Substituent effect, Efecto sustituyente, Etude théorique, Theoretical study, Germanium composé, Germanium compounds, Méthode orbitale moléculaire, Molecular orbital method, Niveau énergie, Energy levels, Résonance magnétique nucléaire, Nuclear magnetic resonance, Germane(chloro triméthyl), and Germane(tétraméthyl)

Germanium chemical shifts were studied theoretically by the ab initio molecular orbital method. The compounds studied were GeMe4-xClx and GeMe4-xHx(x=0-4). The calculated values of the germanium chemical shifts agreed well with the available experimental values. The germanium chemical shift is due to the p-electron mechanism that reflects the ligand electronic effect on the p-p* excitation term in the second-order paramagnetic term. For GeMe4-xHx, the chemical shift is almost linear to the number of the ligand, x. On the other hand, a U-shaped dependence is predicted for the chemical shifts of the GeMe4-xClx series and is shown to be caused by the strong and nonadditive electron-withdrawing ability of the Cl ligand.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Calculs ab initio, Ab initio calculations, Affinité protonique, Proton affinity, Afinidad protónica, Angle liaison, Bond angle, Calcul ab initio, Ab initio calculations, Composé minéral, Inorganic compounds, Distribution charge, Charge distribution, Energie totale, Total energy, Energía total, Etude théorique, Theoretical study, Lithium hydroxyde, Lithium hydroxides, Lithium oxyde, Lithium oxides, Longueur liaison, Bond lengths, Moment dipolaire, Dipole moments, Métal alcalin composé, Alkali metal compounds, Potassium hydroxyde, Potassium hydroxides, Potassium oxyde, Potassium oxides, Sodium hydroxyde, Sodium hydroxides, Sodium oxyde, Sodium oxides, Structure moléculaire, Molecular structure, Li2O, LiNH2, LiOH, Lithium amidure, Na2O, NaOH, Potassium amidure, and Sodium amidure

Ab initio (TZV*, SBK*, and 3-21G* or 6-31G* basis sets) calculations were performed to predict the geometries and gas-phase proton affinities of Li2O, LiOH, LiNH2, Na2O, NaOH, NaNH2, K2O, KOH, and KNH2.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Calculs ab initio, Ab initio calculations, Angle liaison, Bond angle, Etat vibrationnel, Vibrational states, Etude théorique, Theoretical study, Fluorhydrique acide, Hydrofluoric acid, Longueur liaison, Bond lengths, Phosphore composé organique, Organic phosphorus compounds, Spectre IR, Infrared spectra, Spectre Raman, Raman spectra, Structure moléculaire, Molecular structure, and Thiophosphonate(«S-2»-diisopropylaminoéthyl «O»-éthyl méthyl)

We have extended our computations of the structure and of the infrared and Raman spectra of methylphosphonates and related compounds to the O-ethyl S-2-diisopropylaminoethylmethylphosphonothiolate molecule (we abbreviate the name to ESD). We have computed the optimized geometry and the vibrational infrared and Raman frequencies of ESD by means of the Guassian 92 Program Package using 6-31G* basis sets. We assign the vibrational frequencies and we correct each frequency by multiplying it with a previously derived 6-31G* correction factor. The result is a computer-generated prediction of the IR and Raman spectra of ESD. The agreement between our theoretical predictions and the experimental to spectrum of ESD is surprisingly good.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Interactions atomiques et moléculaires: effets sur la structure électronique, Effects of atomic and molecular interactions on electronic structure, Effets d'environnement et effets de solvant, Environmental and solvent effects, Sciences biologiques et medicales, Biological and medical sciences, Sciences biologiques fondamentales et appliquees. Psychologie, Fundamental and applied biological sciences. Psychology, Biophysique moleculaire, Molecular biophysics, Phénomènes intermoléculaires, Intermolecular phenomena, Interactions. Associations, Complexe moléculaire, Molecular complex, Complejo molecular, Eau, Water, Agua, Etude comparative, Comparative study, Estudio comparativo, Etude théorique, Theoretical study, Estudio teórico, Guanine nucléotide, Guanine nucleotide, Guanina nucleótido, Gène onc cellulaire, C-Onc gene, Gen onc celular, Interaction moléculaire, Molecular interaction, Interacción molecular, Produit gène, Gene product, Producto gene, Solution aqueuse, Aqueous solution, Solución acuosa, and Gène ras

High-directional Monte Carlo (HDmC) simulations are performed to investigate the behavior of water molecules in the catalytic sites of human ras p21 proteins and the results are compared among three types of hydrated ras p21 proteins: the normal ras complexed with GDP (normal-p21/GDP), the mutant ras complexed with GDP (mutant-p21/GDP), and the normal ras complexed with GTP (normal-p21/GTP). Also, the original Metropolis Monte Carlo (MMC) simulation is performed on the normal-p21/GDP system. Comparison between HDMC and MMC shows the improved efficeincy of HDMC on this complicated system. Interaction between water molecules is represented by the TIP3P potential function.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs de corrélation électronique pour les atomes et les molécules, Electron correlation calculations for atoms and molecules, Etudes des atomes et molécules particuliers et de leurs ions; agrégats, Studies of special atoms, molecules and their ions; clusters, Macromolécules et polymères, Macromolecules and polymer molecules, Conformation (statistique et dynamique), Conformation (statistics and dynamics), Interatomic distances and angles, Angle liaison, Bond angle, Ascorbique acide, Ascorbic acid, Calcul SCF, SCF calculations, Calcul STO, STO calculations, Composé organique, Organic compounds, Corrélation électronique, Electron correlation, Distribution charge, Charge distribution, Etude théorique, Theoretical study, Hydroxyacide, Hydroxy acids, Hétérocycle oxygène, Heterocyclic oxygen compounds, Liaison hydrogène, Hydrogen bonds, Longueur liaison, Bond lengths, Moment dipolaire, Dipole moments, Stabilité, Stability, Tautomère, Tautomer, Tautómero, and Tétronique acide(hydroxy)

The relative stability of the four tautomeric forms of α-hydroxytetronic acid was calculated with full geometry optimization at the STO-3G, 3-21G, 6-31G*, and 6-31G** SCF levels. Correlation effects were estimated using the MP2 method. Intramolecular hydrogen bonds are found to be of primary importance for the relative stability of the various tautomers, and the same tautomer that in the case of L-ascorbic acid is experimentally observed in the crystal as well as in solution is found to be the most stable one, if polarization functions on the hydrogen atoms are taken into account.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Corrélation électronique, Electron correlation, Etude théorique, Theoretical study, Groupe symétrie, Symmetry groups, Matrice normale, Normal matrix, Matriz normal, Opérateur projection, Projection operators, Représentation irréductible, Irreducible representations, Structure électronique, Electronic structure, Théorie groupe, Group theory, Transformation orthogonale, and Orthogonal transformations

In the present article, improved algorithms for evaluating the irreducible representations of the symmetric group associated with an arbitrary partition, such as the orthogonal, the natural, and the seminormal representation, are introduced and the relations among them are discussed. With the new algorithms, a representation matrix for the orthogonal or the seminormal representation is expressed as the product of three matrices, where two of them are the triangular intrinsic matrices depending on the irreducible representation of the symmetric group; the other relating to the permutation can be given explicitly. Furthermore, we give a concise description for the irreducible representations of the symmetric group and reach an interesting conclusion that the conjugation transformation matrix between the orthogonal and the natural representation is the intrinsic matrix of the symmetric group.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Atome, Atoms, Champ intense, Strong fields, Champ magnétique, Magnetic fields, Energie totale, Total energy, Energía total, Etat fondamental, Ground states, Etude théorique, Theoretical study, Fonction essai, Trial function, Función ensayo, Hélium, Helium, Méthode variationnelle, Variational methods, and He

The helium atom in its ground state, subject to strong magnetic fields, is treated using a variational method. Trial functions consisting of Gaussians with nonlinear parameters variationally optimized are used. The form of these functions is a generalized s-symmetry-state properly modified to admit spatial deformation along the direction on which the magnetic field is applied.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Sciences appliquees, Applied sciences, Physicochimie des polymeres, Physicochemistry of polymers, Polymères organiques, Organic polymers, Composés modèles, Model compounds, Composé alternant, Alternant compound, Compuesto alternante, Etude théorique, Theoretical study, Hydrocarbure aromatique polycyclique, Polycyclic aromatic hydrocarbons, Modèle Hubbard, Hubbard model, Méthode Hartree Fock, Hartree-Fock method, Méthode orbitale moléculaire, Molecular orbital method, Polymère, Polymers, Système électron pi, Pi electron system, and Sistema electrón pi

Within the framework of the AMO-EHF approximation for the Hubbard model, it is shown that the band gap ΔE of an arbitrary regular alternant 1D π-system (polymer), having a singlet ground state, is different from zero, i.e., the ground state is a dielectric one.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Calculs ab initio, Ab initio calculations, Composé organique, Organic compounds, Constante, Constants, Dureté, Hardness, Effet substituant, Substituent effect, Efecto sustituyente, Etude théorique, Theoretical study, Méthode orbitale moléculaire, Molecular orbital method, Niveau énergie, Energy levels, Orbitale frontière, Frontier orbital, Orbital frontera, Structure électronique, Electronic structure, and Benzène dérivé

It is shown that for a number of molecules there exists a Hammett-like equation for the chemical hardness or the HOMO-LUMO energy gap. Substituent effects can be factored out of the molecular hardness. Preliminary results show that a hardness substituent constant, similar to the Hammett α-constant, can be defined and determined for each substituent.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Théorie de la fonctionnelle de densité, Density-functional theory, Dimension base, Basis set size, Dimensión base, Energie totale, Total energy, Energía total, Erreur, Errors, Etude théorique, Theoretical study, Intégrale recouvrement, Overlap integrals, Molécule diatomique, Diatomic molecules, Molécule polyatomique, Polyatomic molecules, Méthode Xalpha, Xalpha method, Método Xalfa, Optimisation, Optimization, Précision, Accuracy, Solution analytique, Analytical solution, Transformation orthogonale, and Orthogonal transformations

The effect of the truncation errors resulting from the numerical integration on the accuracy of the calculation results in the DV-Xα method is analyzed and it is shown that evaluating the overlap integrals analytically or adopting orthogonalized basis sets can reduce the errors on the density matrices to the second order. An approach to improve the calculation accuracy of the total energy is proposed based on the error analysis. The calculation results for several molecules are presented to demonstrate the conclusion.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Théorie de la fonctionnelle de densité, Density-functional theory, Ammoniac, Ammonia, Calcul SCF, SCF calculations, Composé minéral, Inorganic compounds, Dimère, Dimers, Energie liaison, Binding energy, Energie totale, Total energy, Energía total, Etat localisé, Localized states, Etude théorique, Theoretical study, Moment dipolaire, Dipole moments, Méthode fonctionnelle densité, Density functional method, Structure moléculaire, Molecular structure, H N, and NH3

Self-consistent Kohn-Sham density functional calculations have been carried out to study the structure of the ammonia dimer. The local-density approximation yields unusually large binding energy and short internitrogen distance compared with the experimental and more accurate theoretical data. The results from the Becke-Perdew gradient-corrected functionals are generally in good agreement with those at the SCF MP2 level when the geometry is fully optimized with various large basis sets. With our best estimation, the staggered quasi-linear structure (Cs) is 0.6 kcal/mol lower in energy than the symmetric cyclic one (C2h).

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Théorie de la fonctionnelle de densité, Density-functional theory, Atome, Atoms, Champ magnétique, Magnetic fields, Etude théorique, Theoretical study, Ion, Ions, Molécule, Molecules, Mécanique quantique, Quantum mechanics, Méthode Xalpha, Xalpha method, Método Xalfa, Méthode fonctionnelle densité, Density functional method, Spinorbitale, Spinorbital, Orbital spin, Système spin, Spin systems, Théorème viriel, and Virial theorem

The spin virial theorem is derived in the density functional theory. The theorem establishes a relation between the differences of spin-up and -down kinetic and potential energies. The theorem is useful for checking the accuracy of spin orbitals. As an illustration, the example of the Xα method is studied.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Propriétés moléculaires et interactions avec les photons, Molecular properties and interactions with photons, Propriétés des molécules et des ions moléculaires, Properties of molecules and molecular ions, Constantes rotationnelles, vibrationnelles et rovibrationnelles, Rotation, vibration and vibration-rotation constants, Molecular spectra, Vibrational analysis, Atome, Atoms, Etude théorique, Theoretical study, Hydrogène, Hydrogen, Krypton, Modèle, Models, Modelo, Mécanique quantique, Quantum mechanics, Niveau énergie, Energy levels, Oscillateur harmonique, Harmonic oscillators, Porphyrine, Porphyrins, Puits quantique, Quantum wells, Solution analytique, Analytical solution, Spectre IR, Infrared spectra, Spectre énergie, and Energy spectra

A study of two simple quantum mechanical systems, i.e. harmonic oscillator (HO) and hydrogen atom (H) trapped inside the wells is performed. The influence of the spatial confinement on the energy spectra of both systems is investigated. An analytically solvable model of the well potential is presented in the case of the HO. A central and noncentral localization of HO in the well is discussed. The results are used to explain some reported anomalous experimental data on the porphine IR spectrum. The case of hydrogen atom is studied by solving the problem of the electron in the potential V = Z/R cot r/R.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Chimie, Chemistry, Chimie generale et chimie physique, General and physical chemistry, Théorie des réactions, cinétique générale. Catalyse. Nomenclature, documentation chimique, informatique chimique, Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry, Théorie des réactions, cinétique générale, Theory of reactions, general kinetics, Accepteur électron, Electron acceptor, Aceptor electrón, Acide, Acids, Acido, Base, Donneur électron, Electron donor, Donador electrón, Etude théorique, Theoretical study, Estudio teórico, In situ, Potentiel chimique, Chemical potential, Potencial químico, Réactif, Reagents, Reactivo, Réaction chimique, Chemical reaction, Reacción química, Transfert charge, Charge transfer, Transferencia carga, Transfert électron, Electron transfer, and Transferencia electrón

The states of reactants in the donor (base, B)-acceptor (acid, A) systems are examined and the charge transfer (CT) in situ sensitivities, including the chemical potential, hardness, softness, and Fukui function (FF) data, are derived within the atoms-in-molecules (AIM) resolution. Relaxational correction to the reactant CT FF vector is identified and qualitatively examined. The previously introduced intersecting state model (ISM) of the A-B systems is generalized beyond the N-restricted CT energy profile and formulated in terms of the intersecting energy paraboloids of reactants, within both uncoupled (qualitative) and coupled (quantitative) formulations; here, N is the total number of electrons.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Densité électron, Electron density, Eau, Water, Ethanol, Etude théorique, Theoretical study, Molécule, Molecules, Méthanol, Methanol, Méthode mathématique, Mathematical method, Método matemático, Structure moléculaire, Molecular structure, Méthode géométrique, and Méthode topologique

A simple, new technique for the evaluation of the similarity of molecular shapes is presented. The concept of semisimilarity (asymmetric similarity) is applied within the topological- geometrical framework of scaling-nesting similarity measures of molecules. The practical application of these similarity measures is illustrated by the examples of the three-dimensional formal bodies of electronic charge densities of a set of simple molecules.

General chemistry, physical chemistry, Chimie générale, chimie physique, Atomic molecular physics, Physique atomique et moléculaire, Sciences exactes et technologie, Exact sciences and technology, Physique, Physics, Physique atomique et moleculaire, Atomic and molecular physics, Structure électronique des atomes, des molécules et de leurs ions: théorie, Electronic structure of atoms, molecules and their ions: theory, Calculs et techniques mathématiques en physique atomique et moléculaire (sauf les calculs de corrélation électronique), Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations), Calcul variationnel, Variational calculus, Cálculo de variaciones, Champ Coulomb, Coulomb field, Espace Hilbert, Hilbert space, Espace phase, Phase space, Etude théorique, Theoretical study, Fonction propre, Eigenfunctions, Valeur propre, and Eigenvalues

The important duality problem of phase-space representations of quantum mechanics is discussed and the class of self-dual representations is established. It is shown that self-dual phase-space representations may be endowed with a Hilbert space structure resembling the standard picture of quantum mechanics. A stationary variational principle is then formulated, enabling one to solve eigenproblems of observables directly in phase space. A modified, more usable form of this variational principle is also given together with an example of practical application to the 1D Coulomb system.